Non-dispersive conservative regularisation of nonlinear shallow water and isothermal Euler equations

Abstract : A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and possess a variational structure. Thus, the mass, the momentum and the energy are conserved. Hence, for instance, regularised hydraulic jumps are smooth and non-oscillatory. Another particularly interesting feature of this regularisation is that smoothed `shocks' propagates at exactly the same speed as the original discontinuous ones. The performance of the new model is illustrated numerically on some dam-break test cases, which are classical in the hyperbolic realm.
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https://hal.archives-ouvertes.fr/hal-01509445
Contributeur : Denys Dutykh <>
Soumis le : lundi 17 avril 2017 - 21:41:35
Dernière modification le : jeudi 20 avril 2017 - 01:04:39

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Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales 4.0 International License

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  • HAL Id : hal-01509445, version 1
  • ARXIV : 1704.05290

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Didier Clamond, Denys Dutykh. Non-dispersive conservative regularisation of nonlinear shallow water and isothermal Euler equations. 20 pages, 5 figures, 1 table, 34 references. Other author's papers can be downloaded at http://ww.. 2017. <hal-01509445>

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